TIME DOMAIN ACOUSTIC CONTRAST CONTROL IMPLEMENTATION OF SOUND ZONES FOR LOW-FREQUENCY INPUT SIGNALS

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1 TIME DOMAIN ACOUSTIC CONTRAST CONTROL IMPLEMENTATION OF SOUND ZONES FOR LOW-FREQUENCY INPUT SIGNALS Daan H. M. Schellekens 12, Martin B. Møller 13, and Martin Olsen 4 1 Bang & Olufsen A/S, Struer, Denmark 2 Circuits and Systems, Delft University of Technology, Delft, The Netherlands 3 Department of Electronic Systems, Aalborg University, Aalborg, Denmark 4 HARMAN Lifestyle Division, Struer, Denmark d.h.m.schellekens@student.tudelft.nl, mim@bang-olufsen.dk, martin.olsen@harman.com ABSTRACT Sound zones are to or more regions ithin a listening space here listeners are provided ith personal audio. Acoustic contrast control (ACC) is a sound zoning method that maximizes the average squared sound pressure in one zone constrained to constant pressure in other zones. State-of-the-art time domain broadband acoustic contrast control (BACC) methods are designed for anechoic environments. These methods are not able to realize a flat frequency response in a limited frequency range ithin a reverberant environment. Sound field control in a limited frequency range is a requirement to accommodate the effective orking range of the loudspeakers. In this paper, a ne BACC method is proposed hich results in an implementation realizing a flat frequency response in the target zone. This method is applied in a bandlimited lo-frequency scenario here the loudspeaker layout surrounds to controlled zones. The performance is verified ith experimental results in an acoustically damped room. Index Terms Personal sound, sound zones, acoustic contrast control 1. INTRODUCTION Sound zones are regions ithin a listening space here individual audio content is reproduced ithout the requirement for physical separation like earing headphones or moving to adjacent rooms. To create such sound zones, an array of loudspeakers must be controlled, hich is the topic of the presented research. In this paper, the focus is limited to a special scenario ith to zones: a bright zone, here the desired sound is reproduced, and a dark zone ith lo sound pressure relative to the bright zone. This scenario is the simplest building block hich by linear superposition can be used to create multiple spatial regions of individual audio. In this paper, the target frequency range is restricted to lo frequencies. Throughout the audible frequencies, the ave length of sound changes significantly. Due to these changes, different approaches to controlling the sound field are effective in different frequency ranges. Therefore, it can be assumed that a broadband sound zone system can be realized by combining several methods to cover the entire frequency range as proposed in [1] and further exemplified in [2]. Various methods exist to create sound zones. To prominent examples are pressure matching (PM) [3], here both amplitude and phase of a sound field are controlled, and acoustic contrast control (ACC) [4], here the average squared sound pressure in the to zones is controlled. ACC is a sound zoning method here the average squared sound pressure is maximized in the bright zone subject to constant average squared sound pressure in the dark zone. Since only the squared sound pressure is controlled, the phase of the resulting sound field is not controlled. Hoever, the lo-frequency solution, investigated in this paper, should be part of a composite system here it is assumed that sound source localization ill be dominated by the mid and high frequency solutions. Therefore, the phase of the reproduced sound field is not of concern and ACC, ith the higher potential acoustical separation [5], later referred to as contrast, is the focus of this paper. In the early publications [4, 6], ACC is defined at a single excitation frequency, resulting in solutions ith a single complex eight per loudspeaker to create a bright and dark zone simultaneously. Folloing this approach, broadband solutions can be obtained by computing a complex eight at a set of discrete control frequencies. The inverse Fourier transform is utilized in order to create a finite impulse response (FIR) filter. In [7], Cai et al. refer to this approach as traditional acoustic contrast control (TACC). Utilizing TACC results in poor contrast performance at non-control frequencies, making a frequency domain approach ill-suited for broadband systems [7]. Solving the ACC problem for all frequencies simultaneously as an optimization formulated in the time domain is referred to as broadband acoustic contrast control (BACC) and is suggested by Elliott et al. in [8]. In [7], Cai et al. sho that the BACC method results in all frequencies being filtered out, except for a single frequency, thus achieving a high acoustic contrast in the time domain. To realize a flat frequency response in the bright zone the response variation (RV) penalty term is introduced ith the BACC-RV method in [7]. This formulation introduces a reference frequency hich the entire frequency response should match in amplitude. The donside to this method is the requirement of determining a suitable reference frequency leading to an additional optimization. To avoid determining a reference frequency the response differentiation (RD) is introduced as a replacement for the RV-term [9]. The RD-term is a measure of the summed differences beteen neighboring frequency bins in the average frequency response of the resulting sound field in the bright zone. The ork in [9] considers a line array under anechoic conditions hich avoids phenomena like room reflections and loudspeakers surrounding the control region. Such phenomena may cause large variation in the resulting frequency response, hich in turn increases the RD-term. To avoid the RD-term being the dominating term in the optimization in a bandlimited, reverberant scenario, the term must be modified to take the expected variations into account. Reformu /16/$ IEEE 365 ICASSP 2016

2 Listening space Z B Z D 1 2 x s (n) from the source to the k-th microphone in the bright zone can be reritten as y B,k (n) = T r B,k (n), (3) here the superscript T denotes transposition, the coefficient vector is defined as = [ 1(0),..., 1(M 1),..., L(0),..., L(M 1)] T, (4) 3 and the response vector r B,k (n) is expressed as r B,k (n) = [h B,1k (n),..., h B,1k (n M + 1),......, h B,Lk (n),..., h B,Lk (n M + 1)] T. (5) Fig. 1. Setup ith L = 11 oofers and a square grid of 2 2 microphones per zone. lation of the RD-term to a response trend estimation (RTE) term, resulting in a BACC-RTE method, is proposed in this paper. The remainder of this paper is structured as follos: In Section 2, the BACC-RTE method is proposed to overcome the mentioned problems. Experimental results are presented in Section 3 for a surrounding loudspeaker layout in a damped room. The conclusion is given in Section Acoustic contrast 2. THEORY The acoustic contrast beteen to zones, C(Z B, Z D), is defined as the db value of the ratio beteen the average squared sound pressures in the bright and dark zone [4]. Assuming zones of equal size this definition can be ritten as ( Z p(x, t) 2 dtdx ) C(Z B, Z D) = 10 log B 10, (1) Z p(x, t) 2 dtdx D here p is the sound pressure at position x at time instance t and Z B and Z D refer to the spatial region of the bright and dark zone, respectively BACC-RD A schematic of the setup is shon in Fig. 1 here L loudspeakers are driven by a source signal x s(n) filtered by a FIR filter l ith length M. The room impulse response (RIR) of length I beteen the l-th loudspeaker (l = 1, 2,..., L) and the k-th microphone (k = 1, 2,..., B ) in the bright zone is represented by h B,lk (i). The sampled output of the k-th microphone in the bright zone can then be expressed as y B,k (n) = L I 1 M 1 h B,lk (i) l (m)x s(n m i). (2) l=1 i=0 m=0 In this paper, the source signal is assumed to be spectrally hite and thus only the filters l affect the input to the loudspeakers. The pressure at a microphone can therefore be described by the room impulse response from a loudspeaker to the microphone convolved by the filter l for that specific loudspeaker. This can be introduced as x s(n) being the unit sample sequence, hich is assumed throughout this paper. Therefore the total impulse response of length M + I 1 This result can be used to compute the average squared sound pressure in the bright zone as B e B = y 2 B,k(n)/ B = T R B, (6) here R B, the normalized correlation matrix in the bright zone, is expressed as B R B = r B,k (n)r T B,k(n)/ B. (7) Similarly, e D and the associated R D can be defined for the dark zone. To maximize the acoustic contrast in the time domain hile assuming B = D, the BACC method [8] leads to the folloing contrast optimization problem BACC = arg max = arg max e B e D + δ T T (8) R B T R D + δ T, here C(Z B, Z D) from Eqn. (1) is maximized and δ is a parameter to control the penalty on the l 2-norm of BACC in the optimization. In [9] the RD-term is introduced to control the difference in sound pressure beteen neighboring frequency bins. Therefore, the frequency response at the k-th control point in the bright zone is defined as p B,k (f) = y B,k (n)e j2πfnts = T s B,k (f), (9) here T s is the sampling period, f a discrete frequency and s B,k (f) is a ML 1 vector given by s B,k (f) = [r B,k (0),..., r B,k (M + I 2)] [1, e j2πfts,..., e j2πf()ts ] T. (10) This definition of p B,k (f) is then used to calculate RD, hich is defined as the mean square of the first-order differential of the frequency response in the bright zone, and its formulation is given as RD = 1 B (J 1) B f J 1 p B,k (f j+1) p B,k (f j) 2, (11) j=1 here J is the number of discrete frequencies to be controlled and f denotes the frequency resolution. We suggest to pick the set of frequencies {f j} j=1,...,j as a consecutive subset of the discrete Fourier transform (DFT) frequencies, according to the bandlimited 366

3 frequency range of interest. This can be done by neglecting the outer samples of the DFT frequencies. Here, the DFT frequencies are defined as an equally distributed set of M + I 1 frequencies f [0,..., f s f], ith f = s, here fs is the sampling (M+I 1) frequency. To express RD in matrix form, let V = s T B,k(f 1) f , S k =., (12) s T B,k(f J) so that Eqn. (11) using Eqn. (9) can be reritten as RD = T { 1 (J 1) B B { R (VS k ) H (VS k )} }, (13) ith R{ } denoting the real operator and superscript H the Hermitian transpose. When the subset {f j} j=1,...,j equals the complete DFT frequency set S k from Eqn. (13) is the discrete Fourier transform of y B,k (n). The BACC-RD filters are the solution to RD = arg max T R B (1 β) T R D + βrd + δ T, (14) hich is obtained by introducing the RD-term in Eqn. (8) and β is a eight factor beteen 0 and BACC-RTE The RD-term is a function describing the accumulated changes in the resulting average frequency response in the bright zone. In a room, the transfer functions beteen loudspeakers and microphones ill be subject to fluctuations across frequency due to reflections from room boundaries. The RD-term becomes large under such conditions and dominates the denominator in Eqn. (14). Given a limited frequency range of interest, the optimization in Eqn. (14) results in filters ith high attenuation in the target frequency range and high contrast at a single frequency outside this range (as shon in Fig. 2). To overcome this behavior, a ne constraint is proposed to replace the RD-term. The response trend estimation (RTE) term is introduced to reduce the influence of local variations in the resulting frequency response. The RTE-term is a function of the difference beteen the means of to adjacent frequency intervals ith sample length a. It can be ritten as RT E = C0 B f J 2a+1 j=1 p B,k (f j+a) p B,k (f j) p B,k (f j+2a 1) p B,k (f j+a 1) 2, (15) ith C 0 = ( ) 1 (J 2a + 1) B. Instead of V from the RD-term, let a a 0 V a = 1. a 2 f (16) a a be a difference matrix ith dimensions (J 2a+1) J. Each entry in vector V as k is no a sum of a differences instead of a single difference beteen neighboring frequency bins. Each difference is calculated beteen to frequency bins separated by a distance of a f. To compensate for this distance and the number of entries in the sum V a is scaled by (a 2 f) 1. Parameter a should be chosen in a such ay that the smoothing interval a f covers only a small local part of the frequency range of interest. Note that if a = 1, the RTE-term is equal to the RD-term. The RTE-term can no be ritten in matrix form as { B { RT E = T C 0 R (V as k ) H (V as k )} } = T C RT E. (17) This term is used to define the optimization for the BACC-RTE method by RT E = arg max T R B (1 β) T R D + βrt E + δ T. (18) As in [10], Eqn. (18) can be reritten as an eigenvalue problem here the solution is given as the eigenvector of [ (1 β)rd + βc RT E + δi ML ] 1 R B, (19) ith the largest eigenvalue. To ensure the acoustic contrast is optimized only ithin the target frequency range [f 1, f J] it is recommended to filter the RIRs ith a FIR bandpass filter having cut-off frequencies inside the range [f 1, f J]. The filtered RIR can be used in Eqn. (5) to derive R B, R D and C RT E Experimental setup 3. EXPERIMENTAL RESULTS Fig. 1 illustrates the physical experimental setup ith L = 11 oofers in a damped room at Bang & Olufsen (Struer, Denmark). The room is a 279 m 3 room ith reverberation time belo 0.6 s in the investigated frequency range. A set of RIRs from all oofers to B = 4 microphones in the bright and D = 4 microphones in dark zone as measured using sine seeps [11]. The microphones ere arranged in a square grid of 2 2 microphones ith a spacing of 25 cm; approximately covering the size of the human head. The RIRs ere bandpass filtered ith [f lo, f high ] = [20, 300] Hz, f s = 1.2 khz, and I = 150. BACC-RTE filters of length M = 400, ere created ith β = , δ = 10 7, and a = 2. The optimization of RT E ill not give a perfectly flat frequency response in the bright zone. Therefore, equalization is introduced to create a flat frequency response in the frequency range of interest. The gain introduced ith the equalizing filter is beteen 0 and 10 db. The equalization violates the assumption of x s(n) being a unit sample sequence, and as a consequence the resulting contrast is suboptimal Results The results presented in this section are based on to sets of RIRmeasurements in the room described in Section 3.1. The first set of RIRs is used in the optimization for determining the filters. The second set of RIRs is used to evaluate the resulting performance, as presented in Fig. 2 and 3. In Fig. 2 the gray lines sho the four-microphone-average frequency responses in the bright and dark zone hen applying the BACC-RTE method ith the target frequency range [f 1, f J] = 367

4 0 0 Frequency response [db] Frequency response [db] Frequency [Hz] Frequency [Hz] Fig. 2. Averaged frequency responses for BACC-RTE (gray) and BACC-RD (black) method in bright ( ) and dark ( ) zone ith f 1 = 10 Hz and f J = 310 Hz. Fig. 3. Averaged frequency responses for BACC-RTE (gray) and BACC-RD (black) method in bright ( ) and dark ( ) zone ith f 1 = 0 Hz and f J = f s f Hz. [10, 310] Hz, slightly ider than bandpass filter cut-off frequencies. It is observed that an acoustic contrast of almost 30 db is achieved in the majority of the target frequency range. Furthermore, it can be seen that the contrast is optimized only ithin the target frequency range. In Fig. 2 the BACC-RTE response is compared ith the BACC- RD method (plotted in black). It is seen that, contrary to BACC- RTE, the BACC-RD method does not result in the desired flat frequency response, but in a solution that filters out all frequencies except a single frequency component just outside the frequency range of interest. By having almost zero sound pressure in that range the influence of the RD-term is reduced. Frequency responses for both methods ith [f 1, f J] = [0, fs 2 f] are shon in Fig. 3. For the BACC-RD method β is decreased to 0.98 and the RIR length I is increased to 300 to avoid artifacts like the BACC-RD result presented in Fig. 2 due to lo frequency resolution. It is seen that for both methods a flat frequency response is obtained, since it is not possible to optimize the contrast outside the frequency range [f 1, f J]. Hoever, it is generally not of interest to enforce a flat frequency response belo the cut-off frequencies of the loudspeakers. To do so, ould increase the risk of damaging the loudspeakers due to excessive excursion. Hereby, it is sensible to limit the constraint on the response trend to the frequency range here it is of interest to control the sound field. The BACC-RD results in Fig. 2 and 3 are very different because the BACC-RD method is not robust toards only constraining the response differences in a limited frequency range. Hoever, the BACC-RTE results in Fig. 2 and 3 are similar, indicating that the proposed method is robust to constraining the response in a limited frequency range for the optimization. Furthermore, it can be seen from Fig. 3 that the differences beteen the average squared sound pressure in the bright and dark zones are similar, and in a fe areas larger, for the BACC-RTE hen compared to BACC-RD. 4. CONCLUSION The aim of this ork as to create a bandlimited lo-frequency implementation of sound zones using time domain acoustic contrast control. It as shon that previous methods fail to realize a flat frequency response in the desired region in a bandlimited reverberant scenario. The method proposed in this paper overcomes this behavior and achieves a frequency response ithout sudden changes ithin the target frequency range. 5. REFERENCES [1] W. F. Druyvesteyn and J. Garas, Personal sound, Journal of the Audio Engineering Society, vol. 45, no. 9, pp , [2] J. Cheer, S. J. Elliott, and M. F. S. Gálvez, Design and implementation of a car cabin personal audio system, Journal of the Audio Engineering Society, vol. 61, no. 6, pp , [3] M. Poletti, An investigation of 2-d multizone surround sound systems, in Audio Engineering Society Convention 125. Audio Engineering Society, [4] J.-W. Choi and Y.-H. im, Generation of an acoustically bright zone ith an illuminated region using multiple sources, Journal of the Acoustical Society of America, vol. 111, no. 4, pp , [5] P. Coleman, P. J. Jackson, M. Olik, M. Olsen, M. B. Møller, J. A. Pedersen, et al., The influence of regularization on anechoic performance and robustness of sound zone methods, in Proceedings of Meetings on Acoustics. Acoustical Society of America, 2013, vol. 19, p [6] M. Shin, S. Q. Lee, F. M. Fazi, P. A. Nelson, D. im, S. Wang,. H. Park, and J. Seo, Maximization of acoustic energy difference beteen to spaces, The Journal of the Acoustical Society of America, vol. 128, no. 1, pp , [7] Y. Cai, M. Wu, and J. Yang, Design of a time-domain acoustic contrast control for broadband input signals in personal audio systems, in Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on, May 2013, pp [8] S. J. Elliott and J. Cheer, Regularisation and robustness of personal audio systems, ISVR Technical Memorandum 995, University of Southampton, [9] Y. Cai, M. Wu, L. Liu, and J. Yang, Time-domain acoustic contrast control design ith response differential constraint in personal audio systems, The Journal of the Acoustical Society of America, vol. 135, no. 6, pp. EL252 EL257, [10] S. J. Elliott, J. Cheer, J.-W. Choi, and Y. im, Robustness and regularization of personal audio systems, Audio, Speech, and Language Processing, IEEE Transactions on, vol. 20, no. 7, pp ,

5 [11] A. Farina, Advancements in impulse response measurements by sine seeps, in Audio Engineering Society Convention 122. Audio Engineering Society,